Information Technology Reference
In-Depth Information
interconnectedness often cannot be described by analytic functions, as one might expect
from such traditional disciplines as celestial mechanics. In these areas the tying together
of different scales prohibits the taking of derivatives for the definition of functions and,
without any derivatives, it is not possible to construct constitutive equations for describ-
ing the behavior of the phenomenon. This suggests the need for a new way of thinking
about how to represent complex webs.
The entropy measure of complexity can be given a dynamical interpretation, but in
order to do this one has to interpret the dynamics using a probability density. This is
traditionally done by discarding the notion of a closed web and recognizing that every
web has an environment with which it necessarily interacts. By explicitly eliminating
the environmental variables from the description of the web dynamics one obtains a
description that is statistical in nature. The absolute predictability which was appar-
ently present in the deterministic nature of Newton's equations is abandoned for a more
tractable description of the web having many fewer variables, but the price is high and
that price is the loss of absolute predictability. In a general social context the notion of
predicting an outcome is replaced by
anticipating
an outcome.
Implicit in the concept of entropy is the idea of uncertainty. That idea is reasonable
only in a context where there is a conscious being that is extracting information from
the web, and is therefore subjective. Uncertainty means that not all the information one
needs for a complete description of the behavior of a web is available. Even the term
“needs” is in this sense subjective, because it depends on the questions the observer
poses, which in turn depend on the “purpose” of the observer [
26
]. This is where all
subjectivity enters, and we do not go further into the philosophical implications of hav-
ing an observer with a purpose conducting the experiment. We wish merely to be clear
that a web containing conscious individuals cannot be treated in a deterministic way
since the objectivity stemming from determinism conflicts with the subjectivity of the
individual (free will).
However, we can safely say that entropy is a measure of uncertainty as it relates to
order in a physical network, and, like uncertainty, entropy is a non-decreasing func-
tion of the amount of information available to the observer. This connection between
information and statistical physics is quite important, and at this stage of our dis-
cussion we can say that it is the uncertainty that allows us to describe dynamical
webs in thermodynamic terms. Szilard [
31
] was the first to identify information with
entropy in his explanation of why Maxwell's demon does not violate the second law of
thermodynamics.
Perhaps we should say a few words here about phase space and what it is. We under-
stand physical space to be what we measure with a ruler and a clock, the space-time
continuum. However, historically, in trying to understand the behavior of complex sys-
tems physicists realized that it was necessary to know the position and momentum of
every particle of that system, say of a gas. Therefore, consider a space in which the
coordinate axes are the positions and momenta of all the particles, and consequently
the “phase” or state of the complex system is specified by a single point in this space.
In this way the dynamics of the gas could be described by a single trajectory in this
high-dimensional space as the gas diffuses through the room or undergoes any other
